Issn (Print) 2319 5940 International Journal of Advanced Research in Computer and Communication Engineering iso 3297: 2007 Certified

II. ECG SIGNAL FILTERING 
Electrocardiographic signals may be recorded on a long 
timescale (i.e., several days) for the purpose of identifying 
intermittently occurring disturbances in the heart rhythm. 
As a result, the produced ECG recording amounts to huge 
data sizes that quickly fill up available storage space [6]. 
Transmission of signals across public telephone networks 

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IJARCCE 
ISSN (Online) 2278-1021 
ISSN (Print) 2319 5940 
 
International Journal of Advanced Research in Computer and Communication Engineering 
ISO 3297:2007 Certified 
Vol. 5, Issue 9, September 2016 
Copyright to IJARCCE 
DOI 10.17148/IJARCCE.2016.5993
439 
is another application in which large amountsof data are 
involved. For both situations, data compression is an 
essential 
operation 
and, 
consequently, 
represents 
yetanother objective of ECG signal processing. Signal 
processing has contributed significantly to a new 
understanding of the ECG and its dynamic propertiesas 
expressed by changes in rhythm and beat morphology [7]. 
A. ADAPTIVE FILTERING 
Adaptive filtering involves the change of filter parameters 
(coefficients) over time. It adapts to the change in signal 
characteristics in order to minimize the error. It finds its 
application in adaptive noise cancellation, system 
identification, frequency tracking and channel equalization 
[8]. Fig. 2 shows the general structure of an adaptive filter. 
Fig.2 Adaptive filter structures 
In Figure 2, x(n) denotes the input signal. The vector 
representation of x (n) is given where in Equation 1. This 
input signal is corrupted with noises. In other words, it is 
the sum of desired signal d(n) and noise v(n), as 
mentioned in Eq.1. here, The input signal vector is x (n) 
which is given by 
x(n)

[( n), x ( n 

1),.......x ( n 

N

1)]
T
1 
x(n)

d ( n)

v ( n) 2 
The adaptive filter has a Finite Impulse Response (FIR) 
structure. For such structures, the impulse response is 
equal to the filter coefficients. The coefficients for a filter 
of order N are defined as in equation 3. 
W ( n)

[ w (0), w (1), ......w ( N

1)]
T
3 
n
n
N
The output of the adaptive filter is y(n) which is given by 
in equation 4. 
y(n)

W ( n)
T
x ( n) 4 
The error signal or cost function is the difference between 
the desired and the estimated signal is represented in 
equation 5. 
e(n)

d(n)

y ( n) 5 
Moreover, the variable filter updates the filter coefficients 
at every time instant is shown in equation 6. 
W(n

1)

W ( n)

W ( n) 6 
Where, ∆W(n) is a correction factor for the filter 
coefficients. The adaptive algorithm generates this 
correction factor based on the input and error signals [9]. 
B. Adaptive Algorithms 
In adaptive filters, the weight vectors are updated by an 
adaptive algorithm to minimize the cost function. The 
algorithms used by us for noise reduction in ECG in this 
thesis are least mean square (LMS), Normalized least 
mean square (NLMS), sign data least mean square 
(SDLMS), sign error least mean square (SELMS) and 
sign-sign least mean square (SSLMS) algorithms. 
(a) LMS algorithm 
It is a stochastic gradient descent method in which the 
filter weights are only adapted based on the error at the 
current time. According to this LMS algorithm the updated 
weight is given in equation 7. 
W(n 

1)

W ( n)

2.

.x( n).e( n) 7
Where, µ is the step size. 
(b) NLMS algorithm 
The NLMS algorithm is a modified form of the standard 
LMS algorithm. The NLMS algorithm updates the 
coefficients of an adaptive filter by using the following 
equation 8. 
W (n

1)

W ( n)

2.

. (x( n)/ || x ( n) ||
2
).e(n)8 
Eq. 8 can be rewritten as 
W (n

1)

W( n)

2.

( n).x( n).e( n) 9 
From Eq. 7 and Eq. 9, the NLMS algorithm becomes the 
same as the standard LMS algorithm except that the 
NLMS algorithm has a time-varying step size μ (n). This 
step size improves the convergence speed of the adaptive 
filter. 
(c) SDLMS algorithm 
In SDLMS algorithm, the sign function is applied to the 
input signal vector x(n). This algorithm updates the 
coefficients of an adaptive filter using the following 
equation 10. 
W (n

1)

W( n)

2.

.sgn( x( n)).e( n) 10 
(d) SELMS algorithm 
In SELMS, the sign function is applied to the error signal 
e(n). This algorithm updates the coefficients of an adaptive 
filter using the following equation 11. 
W (n

1)

W (n)

2.

.x( n).sgn(e( n)) 11 

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